A new Labor leader would have to put their claim to the prime ministership to the test with a confidence vote in the parliament, the independent MP Rob Oakeshott has said.

Oakeshott said he would decide his position in any confidence vote on the basis of the policies advocated, and as yet from Kevin Rudd he had seen none.

The Greens have also said a leadership change would raise the possibility of going straight to an election rather than supporting a different Labor leader as prime minister.

As Labor is again consumed by leadership speculation, the added complication of a hung parliament has raised constitutional questions.

In a late-night parliamentary speech on Monday, Oakeshott made an “open statement” to the governor general, Quentin Bryce, who would ultimately have to decide which leader, if any, was able to form a government, urging her not to assume the independents would automatically support a new Labor leader.

“We have still more rumours from those formally and informally stalking Julia Gillard as commissioned prime minister. I want to address this tonight in an open statement to the governor general,” Oakeshott said.

“I invite the governor general to assume nothing. I do not automatically support any political party. I support policy for the nation. I make decisions in this parliament, on nothing other than the policies,” he said, nominating road funding, Indigenous constitutional recognition, tax reform, education funding and asylum policies as examples of things he thought were important.

He said Julia Gillard “has a view on all of these” and “if anyone thinks they can do better, I invite them to put their policies to the floor of the parliament”.

But Oakeshott also had an angry assessment of some of critics – including those in the Coalition – who had run down the hung parliament, saying he “questioned the loyalty to the nation” of people so “wedded to their party of choice that they opt to hate their parliament if their party does not control it”.

“Since when has disrespecting a parliament, rather than respecting a parliament, been an act of loyalty? Since when is disrespecting the office of prime minister, rather than respecting the office of prime minister, seen as an act of loyalty? Since when is verballing and patronising electors, that they somehow got it wrong in 2010 rather than respecting the result, seen as an act of loyalty?” he said.

“Of course, none of these are acts of loyalty at any level. They are the acts and views of radicals. And many, too many, have fallen into this lazy world of spit and venom at the expense of nation-building and investing respectfully in our institutions that are the foundation of our democracy.”

Oakeshott and fellow independents Andrew Wilkie and Tony Windsor allowed Julia Gillard to form government after the 2010 election, along with the Greens lower house MP Adam Bandt.